Preheat a gas grill or build a charcoal fire for direct grilling.
Cut the watermelon in half lengthwise, then cut each half in half. Cut these quarters into 2-inch-thick slices. Brush the slices lightly with olive oil and set aside until ready to grill.
Combine lime and orange juices. Taste; if it is too tart, add more orange juice. It should taste like a “sour” orange. Add the salt and cayenne and whisk continually while adding the oil in a thin stream. Whisk until thickened (emulsified). Taste and adjust the oil and salt to your liking. Add the mint and set aside.
Just before serving, place the oiled watermelon slices on a very clean cooking grate directly over the heat source. Grill until marked and just warmed through but still crunchy, 2 to 3 minutes per side. Let cool.
Cut off the rinds and discard. Cut the watermelon into chunks and place in a serving bowl. Pour the dressing over the top and toss gently. Top with the feta, if desired, and sprinkle with another pinch of cayenne.
Photo: Christopher Hirsheimer